The Finite Difference Time Domain (FDTD) Method to Determine Energies and Wave Functions of Two-Electron Quantum Dot

The finite difference time domain (FDTD) method has been successfully applied to obtain energies and wave functions for two electrons in a quantum dot modeled by a three dimensional harmonic potential. The FDTD method uses the time-dependent Schr\"odinger equation (TDSE) in imaginary time. The TDSE is numerically solved with an initial random wave function and after enough simulation time, the wave function converges to the ground state wave function. The excited states are determined by using the same procedure for the ground state with additional constraints that the wave function must be orthogonal with all lower energy wave functions. The numerical results for energies and wave functions for different parameters of confinement potentials are given and compared with published results using other numerical methods. It is shown that the FDTD method gives accurate energies and wave functions.